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[01:11:03] Is there a metric on [math]\displaystyle{ U^14 }[/math]. Well, we both want one and don't want one. If we had a metric from the space of all metrics, we could define Fermions, but we would also lock out any ability to do dynamics. We want some choice over what this metric is, but we don't want full choice because we want enough to be able to define the matter fields to begin with.
[01:11:22] It turns out. That if this is [math]\displaystyle{ X^4 }[/math]
[01:11:29] and this is this particular indogenous choice of [math]\displaystyle{ U^14 }[/math] we have a 10 dimensional metric along the fibers. So we have a [math]\displaystyle{ G^{10}_{\mu nu} }[/math]. Further for every point in the fibers, we get a metric downstairs on the base space. So if we pull back the cotangent bundle,
[01:11:59] we get a metric [math]\displaystyle{ G^4_{\mu \nu} }[/math] on [math]\displaystyle{ \Pi^* }[/math] star of the cotangent bundle of X. We now define the chimeric bundle, right? And the chimeric bundle. Is this direct, some of the vertical tangent bundle along the fibers with the pullback, which we're going to call the horizontal bundle from the base space. So the chimeric bundle